The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Dessins d'enfants and hubbard trees”

Conservative polynomials and yet another action of Gal ( ℚ ¯ / ℚ ) on plane trees

Fedor Pakovich (2008)

Journal de Théorie des Nombres de Bordeaux

Similarity:

In this paper we study an action D of the absolute Galois group Γ = Gal ( ℚ ¯ / ℚ ) on bicolored plane trees. In distinction with the similar action provided by the Grothendieck theory of “Dessins d’enfants” the action D is induced by the action of Γ on equivalence classes of conservative polynomials which are the simplest examples of postcritically finite rational functions. We establish some basic properties of the action D and compare it with the Grothendieck action.

Dynamics on Hubbard trees

Lluís Alsedà, Núria Fagella (2000)

Fundamenta Mathematicae

Similarity:

It is well known that the Hubbard tree of a postcritically finite complex polynomial contains all the combinatorial information on the polynomial. In fact, an abstract Hubbard tree as defined in [23] uniquely determines the polynomial up to affine conjugation. In this paper we give necessary and sufficient conditions enabling one to deduce directly from the restriction of a quadratic Misiurewicz polynomial to its Hubbard tree whether the polynomial is renormalizable, and in this case,...

Introduction to Iterated Monodromy Groups

Sébastien Godillon (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

The theory of iterated monodromy groups was developed by Nekrashevych [9]. It is a wonderful example of application of group theory in dynamical systems and, in particular, in holomorphic dynamics. Iterated monodromy groups encode in a computationally efficient way combinatorial information about any dynamical system induced by a post-critically finite branched covering. Their power was illustrated by a solution of the Hubbard Twisted Rabbit Problem given by Bartholdi and Nekrashevych...

Hubbard trees

Alfredo Poirier (2010)

Fundamenta Mathematicae

Similarity:

We provide a full classification of postcritically finite polynomials as dynamical systems by means of Hubbard trees. The information encoded in these objects is solid enough to allow us recover all the relevant statical and dynamical aspects of the corresponding Julia sets.